Heavy-hadron molecular spectrum from light-meson exchange saturation

TL;DR

This paper models the spectrum of heavy-hadron molecules using light-meson exchange saturation, successfully explaining known states and predicting new molecular states, including a potential explanation for the Y(4260).

Contribution

It introduces a contact-range theory saturated by light mesons to predict and interpret heavy-hadron molecular spectra, connecting experimental states with theoretical models.

Findings

Successfully postdicts the X(3872) as a D* D molecule from pentaquark data.

Predicts a D D̄₁ molecule at 4240-4260 MeV, possibly related to Y(4260).

Reproduces deuteron and virtual state masses using SU(4)-Wigner symmetry.

Abstract

If known, the spectrum of heavy-hadron molecules will be a key tool to disentangle the nature of the exotic states that are being discovered in experiments. Here we argue that the general features of the molecular spectrum can be deduced from the idea that the short-range interaction between the heavy hadrons is effectively described by scalar and vector meson exchange, i.e. the $\sigma$, $\omega$ and $\rho$ mesons. By means of a contact-range theory where the couplings are saturated by the aforementioned light mesons we are indeed able to postdict the $X(3872)$ (as a $D^* \bar{D}$ molecule) from the three $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ pentaquarks (as $\bar{D}\Sigma_c$ and $\bar{D}^* \Sigma_c$ molecules). We predict a $J^{PC} = 1^{--}$ $D \bar{D}_1$ molecule at $4240-4260\,{\rm MeV}$ which might support the hypothesis that the $Y(4260)$ is at least partly molecular. The extension of these ideas to the light baryons requires minor modifications, after which we recover approximate SU(4)-Wigner symmetry in the two-nucleon system and approximately reproduce the masses of the deuteron and the virtual state.